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New theories and applications of tempered fractional differential equations

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A Correction to this article was published on 13 July 2021

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Abstract

In this paper, we develop theories, properties and applications of a new technique in tempered fractional calculus called the Tempered Fractional Natural Transform Method. This method can be used to solve a myriad of problems in tempered fractional linear and nonlinear ordinary and partial differential equations in both the Caputo and Riemann–Liouville senses. We prove some theorems and establish related properties of the Tempered Fractional Natural Transform Method. We give exact solutions, with graphical illustrations, to three well-known problems in tempered fractional differential equations including a special case of Langevin equation. Our results are the first rigorous proofs of Tempered Fractional Natural Transform Method. Further, the present work can be considered as an alternative to existing techniques, and will have wide applications in science and engineering fields.

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Acknowledgements

The authors are appreciative for anonymous referees for their hard work reading the paper and for their recommendations to improve the manuscript.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Vermont, Burlington, VT, 05405, USA

    Nazek A. Obeidat & Daniel E. Bentil

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  1. Nazek A. Obeidat
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  2. Daniel E. Bentil
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Correspondence to Nazek A. Obeidat.

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Funding

NAO was supported in part by graduate teaching assistantship from the University of Vermont. DEB was supported in part by a Fulbright Scholar Fellowship (PS00289132), Carnegie African Diaspora Fellowship (P00214069), and the University of Vermont through a sabbatical leave.

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The authors declare that they have no conflict of interest concerning the publication of this manuscript.

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Theorem (4.2) has been updated. The original article has been corrected.

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Obeidat, N.A., Bentil, D.E. New theories and applications of tempered fractional differential equations. Nonlinear Dyn 105, 1689–1702 (2021). https://doi.org/10.1007/s11071-021-06628-4

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